1. Vertical Datums and Heights
Daniel J. Martin
National Geodetic Survey
VT Geodetic Advisor
VTrans Monthly Survey Meeting
October 06, 2008

2. Can You Answer These Questions?
What is the current official vertical datum of the United States?
What’s the difference between ellipsoid, orthometric and geoid and dynamic heights?
The difference between NGVD 29 and NAVD 88 in most of Vermont is?
A point with a geoid height of m means what?

4. GEODETIC DATUMS
A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth. Specific geodetic datums are usually given distinctive names. (e.g., North American Datum of 1983, European Datum 1950, National Geodetic Vertical Datum of 1929)
Characterized by:
A set of physical monuments, related by survey measurements and resulting coordinates (horizontal and/or vertical) for those monuments

5. GEODETIC DATUMS CLASSICAL Contemporary
Horizontal – 2 D (Latitude and Longitude) (e.g. NAD 27, NAD 83 (1986))
Vertical – 1 D (Orthometric Height) (e.g. NGVD 29, NAVD 88)
Contemporary
PRACTICAL – 3 D (Latitude, Longitude and Ellipsoid Height) Fixed and Stable – Coordinates seldom change (e.g. NAD 83 (1992) or NAD 83 (NSRS 2007))
SCIENTIFIC – 4 D (Latitude, Longitude, Ellipsoid Height, Velocity) – Coordinates change with time (e.g. ITRF00, ITRF05)

6. (MSL, MLLW, MLW, MHW, MHHW etc.)
Vertical Datums
A set of fundamental elevations to which other elevations are referred.
Datum Types
Tidal – Defined by observation of tidal variations over some period of time
(MSL, MLLW, MLW, MHW, MHHW etc.)
Geodetic – Either directly or loosely based on Mean Sea Level at one or more points at some epoch
(NGVD 29, NAVD 88, IGLD85 etc.)

7. TYPES OF HEIGHTS ORTHOMETRIC GEOID ELLIPSOID DYNAMIC
The distance between the geoid and a point on the Earth’s surface measured along the plumb line.
GEOID
The distance along a perpendicular from the ellipsoid of reference to the geoid
ELLIPSOID
The distance along a perpendicular from the ellipsoid to a point on the Earth’s surface.
DYNAMIC
The distance between the geoid and a point on Earth’s sruface measured along the plumb line at a latitude of 45 degrees

8. Orthometric Heights Using Optical or Digital/Bar Code Leveling
Topography
Adjusted to Vertical Datum using existing control
Achieve 3-10 mm relative accuracy
Using Optical or Digital/Bar Code Leveling
Begin our understanding of orthometric heights.
Heights & Datums - traditionally orthometric heights meant above sea level. Now we must be aware of factors affecting our understanding and use of height interpretations.
Determining elevation differences through use of conventional leveling procedures. Conventional spirit-leveled height from points A to B and B to C.
Differential leveling surveys, being a “piecewise” metric measurement technique, accumulate local height differences (dh).

9. VERTICAL DATUMS OF THE UNITED STATES
First General Adjustment – 1899
(a.k.a. – Sandy Hook Datum)
Second General Adjustment
Third General Adjustment
Fourth General Adjustment
There have been several different ellipsoids used for the horizontal datums of the United States. The Bessell 1841 ellipse was used from approximately 1845 until Clarke 1866, developed by the English Geodesist A. R. Clarke was adopted in 1879 following the completion of the great Transcontinental Arc of Triangulation as it most closely approximates the size and shape of North America. As part of the activity to complete the North American Datum of 1983 (NAD 83), In 1979, the National Geodetic Survey decieded to adopt the Geodetic Reference System 1980 (GRS 80) as recommended by the International Association of Geodesy, as it most closely reflects the size and shape of the entire globe. It should be noted that GRS80 is for all practical purposes, the same size and shape as the World Geodetic System of 1984 (WGS 84) ellipsoid used with the Global Positioning System (GPS). The small numerical differences in the flattening (1/f) amount to less than 0.1 millimeter from the most northern part of Alaska to the southern tip of Florida!!
Mean Sea Level 1929
National Geodetic Vertical Datum of 1929 (NGVD 29)
North American Vertical Datum of 1988 (NAVD 88)

10. NGVD 29 TIDE CONTROL
As much as 5 feet – or a meter and a half, even 2 meters in some areas, with most of it in the Rockies.

11. Orthometric Heights Comparison of Vertical Datum Elements
NGVD NAVD 88
DATUM DEFINITION TIDE GAUGES FATHER’SPOINT/RIMOUSKI
IN THE U.S. & CANADA QUEBEC, CANADA (BM 1250-G)
TIDAL EPOCH Varies from point-to-point
BENCH MARKS , ,000
LEVELING (Km) , ,001,500
GEOID FITTING Distorted to Fit MSL Gauges Best Continental Model
This shows the differences in the components of the vertical datums.
The datum is not just the values, but the way the computations are done.

12. As much as 5 feet – or a meter and a half, even 2 meters in some areas, with most of it in the Rockies.

13. 3-D Coordinates derived from GNSSX1 Y1 Z1 X2 Y2 Z2 X3 Y3 Z3 X4 Y4 Z4 Z XA YA ZA A hA A A NA EA hA
Greenwich
Meridian
Earth
Mass Center
+ZA
+ GEOID03 +
- Y A HA A YA
- X NA EA HA XA Y X
Equator
- Z

14. What is the GEOID?
“The equipotential surface of the Earth’s gravity field which best fits, in the least squares sense, mean sea level.”*
Can’t see the surface or measure it directly.
Modeled from gravity data.
*Definition from the Geodetic Glossary, September 1986

15. -although GSFC00.1 created significant changes when looking at the difference between G99SSS and USGG2003, the magnitude of those differences is dwarfed by the total signal

16. Relationships Geoid = global MSL Average height of ocean globally
Where it would be without any disturbing forces (wind, currents, etc.).
Local MSL is where the average ocean surface is with the all the disturbing forces (i.e., what is seen at tide gauges).
Dynamic ocean topography (DOT) is the difference between MSL and LMSL:
LMSL = MSL + DOT
-Additionally, lidar observations on the open ocean can be reduced as well in VDatum areas where the tides are known.
-Only temporal effects due transient weather will remain unmodeled – and generally you don’t fly in adverse weather.
Ellipsoid
LMSL
Geoid N
Tide gauge height
DOT

17. ELLIPSOID - GEOID RELATIONSHIP
H = Orthometric Height (NAVD 88)
h = Ellipsoidal Height (NAD 83)
H = h - N
N = Geoid Height (GEOID 03) H
TOPOGRAPHIC SURFACE h N
GEOID 03
Geoid
Ellipsoid
GRS80

18. Level Surfaces and Orthometric Heights
Earth’s
Surface WP
Level Surfaces P
Plumb
Line
Mean
“Geoid”
Sea
Level WO PO
Level surfaces - imagine earth standing still - ocean standing still; no effects such as currents, tides, winds; except for slight undulations created by gravity effects = level surface.
Geoid is this level surface relating to today’s mean sea level surface - this does not truly coincide with mean sea level because of the non-averaging effects of currents, tides, water temperatures, salinity, weather, solar/lunar cycle, etc. The geoid is a best fit mean sea level surface.
Equipotential surfaces - add or subtract water and level surface changes parallel to previous surface = infinite number of possible level surfaces. Each equipotential surface has one distinct potential quantity along its surface.
Point on earth’s surface is the level surface parallel to the geoid achieved by adding or subtracting potential. Lines don’t appear parallel; they are based on the gravity field and are affected by mass pluses and minuses.
Geopotential number is the numerical difference between two different equipotential surfaces. W = potential along a level surface. CP = geopotential number at a point.
Plumb line (over exaggerated in drawing) - is a curved distance due to effects of direction of gravity- known as deflection of the vertical.
Orthometric height is exactly the distance along this curved plumb line between the geoid and point on the earth’s surface. We can make close approximations but to be exact we would need to measure gravity along this line requiring a bored hole which is impractical.
Level Surface = Equipotential Surface (W)
Ocean
Geopotential Number (CP) = WP -WO
H (Orthometric Height) = Distance along plumb line (PO to P)

19. Leveled Height vs. Orthometric Height
 h = local leveled differences
H = relative orthometric heights
Equipotential Surfaces B
Topography
 hAB
=  hBC A C HA HC
HAC  hAB + hBC
Reference Surface (Geoid)
Observed difference in orthometric height, H, depends on the leveling route.

20. Tectonic Motions

21. PRELIMENARY Vertical Velocities: CORS w/ <2.5 yrs data

22. PRELIMENARY North American Vertical Velocities

23. High Resolution Geoid Models GEOID03 (vs. Geoid99)
Begin with USGG2003 model
14,185 NAD83 GPS heights on NAVD88 leveled benchmarks (vs 6169)
Determine national bias and trend relative to GPS/BMs
Create grid to model local (state-wide) remaining differences
ITRF00/NAD83 transformation (vs. ITRF97)
Compute and remove conversion surface from G99SSS
GEOID99 - best model for North America; not as true interpretation of the geoid but includes bias to establish best orthometric heights.
G99SSS + GPS/levels augmentation = GEOID99
6169 GPS/levels bench marks (NAD83/NAVD88); more to be included to further improve future models. GPS/BM constrained to help model reflect NAVD88 orthometric heights then unconstrained for final model.
NAD83 non-COM - model warped to reflect NAD83 (86) non-COM origin.
4.6 cm RMS ( 9.2 cm absolute geoid height) when comparing to bench mark data.

24. High Resolution Geoid Models GEOID03 (vs. Geoid99)
Relative to non-geocentric GRS-80 ellipsoid
2.4 cm RMS nationally when compared to BM data (vs. 4.6 cm)
RMS  50% improvement over GEOID99 (Geoid96 to 99 was 16%)
GEOID06 ~ By end of FY07
GEOID99 - best model for North America; not as true interpretation of the geoid but includes bias to establish best orthometric heights.
G99SSS + GPS/levels augmentation = GEOID99
6169 GPS/levels bench marks (NAD83/NAVD88); more to be included to further improve future models. GPS/BM constrained to help model reflect NAVD88 orthometric heights then unconstrained for final model.
NAD83 non-COM - model warped to reflect NAD83 (86) non-COM origin.
4.6 cm RMS ( 9.2 cm absolute geoid height) when comparing to bench mark data.

25. Plot of 6169 GPS/levels bench marks used in Geoid99 model; overrides gravity information by computing model relative to GPS/NAVD88 bench marks.
NAVD88 to Geoid99 - comparisons between level surfaces; 31 cm NAVD88 bias is consistent around U.S. reflecting the difference determined at Father Point, Rimouski. This shows that the error at any given point is fairly relative to the error at another point.

27. H = h - N
m = m - ( m)
m ≠ m
(0.18 m/0.06 ft) H h N

28. VERTCON - Vertical Datum Transformations
Published = m
Difference = m / ft

29. www.ngs.noaa.gov Available “On-Line” at the NGS Web Site:
Guidelines - will eventually become routine; not so much explanation of why its done but provides background information. Repeat baselines, station spacing, fixed height antenna setups, identify and control all error sources, tie local networks together, etc..
NOS NGS-58 GPS-Derived Ellipsoid Heights Guidelines will lay the foundation for GPS-Derived Orthometric Heights Guidelines. Produce 2 cm ellipsoid heights to be able to obtain 2 cm orthometric heights.

30. Using the Differential Form
Using the difference eliminates bias
Assumes the geoidal slopes “shape” is well modeled in the area.
“Valid” Orthometric constraints along with “valid” transformation parameters removes additional un-modeled changes in slope or bias (fitted plane)

31. Two Days/Same Time -10.254 -10.251 > -10.253 Difference = 0.3 cm
>
Difference = 0.3 cm
“Truth” =
Difference = 2.3 cm
Two Days/
Different Times
>
Difference = 4.1 cm
Dh is computed for a series of 30 minute sessions over 2 days and the average dh is found
Taking the observation from the same time each day (when the satellite geometry is similar), the difference in the dh is only .3 cm, but the difference from the average is 2.3 cm.
Now if you take the dh from different times on the 2 days (different geometry), the difference between the 2 vectors is 4.1 cm, but the difference from the average is only .1 cm
“Truth” =
Difference = 0.1 cm

32. What is OPUS? On-Line Positioning User Service
Processes Dual-Frequency GPS data
Global availability (masked)
3 goals:
Simplicity
Consistency
Reliability

33. How Does OPUS Compute Position?
NGS-PAGES software used
L3-fixed solution w/ tropo adjusted
3 “best” CORS selected 3 separate baselines computed 3 separate positions averaged
Position differences also include any errors in CORS coordinates

34. To enhance vertical accuracy use rapid orbits available in 24 hours
HOW GOOD ARE OPUS ORTHOMETRIC HEIGHTS?
IT DEPENDS!
ORTHOMETRIC HEIGHT ~ 0.02 – 0.04 m
GEOID03 ~ m (2 sigma – 95% confidence)
Error ~
~ 0.08 m
PUBLISHED
(0.009 m)
(0.005 m) m
To enhance vertical accuracy use rapid orbits available in 24 hours
Broadcast Orbits ~ 5 m (real time)
Ultrarapid Orbits ~ m (12 hours)
Rapid Orbits ~ 0.01 – 0.02 m (24 hours)
Precise Orbits ~ – 0.01 m (two weeks)

35. Gravity Recovery And Climate Experiment (GRACE)

36. Gravity Recovery And Climate Experiment (GRACE)

37. Absolute gravimeter: Example: Micro-g Solutions FG5
Ballistic (free-fall) of retro- reflector in vacuum chamber, tracked by laser beam
Instrument accuracy and precision: ± 1.1 mGals
Used for temporal change of g 7

38. Spring-based relative gravimeters Example: LaCoste & Romberg land meter
A mass at end of a moment arm is suspended by spring
Number of screw turns necessary to null position of mass gives change in g from reference sta.
Accuracy: ± 3 to 50 mGals 5

40. Changes for the Better Improve Gravity Field Modeling
NGS will compute a pole-to-equator, Alaska-to-Newfoundland geoid model, preferably in conjunction with Mexico and Canada as well as other interested governments, with an accuracy of 1 cm in as many locations as possible
NGS redefines the vertical datum based on GNSS and a gravimetric geoid
NGS redefines the national horizontal datum to remove gross disagreements with the ITRF